The shooting was contained to the Firebirds Wood Fired Grill restaurant in the La Encantada mall in Tucson, said Pima County Sheriff's Department spokesman Cody Gress.
One woman was injured with a gunshot to the leg and was treated at a local hospital, Gress said.
On Saturday, the sheriff's department described the shooting as an apparent murder-suicide. The shooting suspect was identified as Frederick Bair, 60, who died of a self-inflicted gunshot wound, the department said.
He was a captain with the Tucson Fire Department, the agency's spokesman said in a news release.
Bair's ex-wife, Mary Jo Bair, was wounded. And a male victim, 65-year-old Eliot Cobb, died.
"It looked like two gentlemen were fighting, it was hard to tell," witness Laura Harder told CNN affiliate KGUN-TV
in Tucson. "I saw a gun come out and he just shot him in the head right in front of us."
Harder said the restaurant was full when she noticed something was happening at a nearby table. After the shooting, she saw how the gunman grabbed the other man's companion by the arm and pushed her down a hallway.
Harder heard two more gunshots while crawling on the ground for an exit.
"I assumed he had shot her," she said.
As gunshots erupted, patrons began screaming and running out of the restaurant.
Toni Esquibel was celebrating her daughter's 13th birthday with family and friends. They had just been served their meals when the commotion began and they took cover under their table.
"There were probably about 10 shots. It was pretty harrowing. Pretty harrowing, not fun for young girls to have to go through that kind of experience," Esquibel told CNN affiliate KOLD-TV